Channel tracking with scattered pilots

ABSTRACT

According to the disclosure, a system adapted to estimate and track a channel for wireless orthogonal frequency division modulation (OFDM) communication is disclosed. The system utilizes scattered pilot symbols being subject to channel conditions and estimates the channel value using the plurality of received pilot symbols and in accordance with correlation of the channel conditions over time.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation and claims priority to U.S.patent application Ser. No. 11/182,089, filed Jul. 14, 2005, entitled“Channel Tracking with Scattered Pilots” and which claims priority toU.S. provisional application No. 60/588,599, filed Jul. 16, 2004,entitled “Channel Tracking with Scattered Pilots”, now abandoned, bothof which can be assigned to assignee hereof and hereby expresslyincorporated by reference herein.

BACKGROUND OF THE DISCLOSURE

The present disclosure relates to wireless digital communication systemsand, amongst other things, to estimation of channel characteristics andinterference level in such systems.

Demand for wireless digital communication and data processing systems ison the rise. Inherent in most digital communication channels are errorsintroduced when transferring frames, packets or cells containing data.Such errors are often caused by electrical interference or thermalnoise. Data transmission error rates depend, in part, on the mediumwhich carries the data. Typical bit error rates for copper based datatransmission systems are in the order of 10⁻⁶. Optical fibers havetypical bit error rates of 10⁻⁹ or less. Wireless transmission systems,on the other hand, may have error rates of 10⁻³ or higher. Therelatively high bit error rates of wireless transmission systems posecertain difficulties in encoding and decoding of data transmitted viasuch systems. Partly because of its mathematical tractability and partlybecause of its application to a broad class of physical communicationchannels, the additive white Gaussian noise (AWGN) model is often usedto characterize the noise in most communication channels.

Data is often encoded at the transmitter, in a controlled manner, toinclude redundancy. The redundancy is subsequently used by the receiverto overcome the noise and interference introduced in the data whilebeing transmitted through the channel. For example, the transmittermight encode k bits with n bits where n is greater than k, according tosome coding scheme. The amount of redundancy introduced by the encodingof the data is determined by the ratio n/k, the inverse of which isreferred to as the code rate. Codewords representing the n-bit sequencesare generated by an encoder and delivered to a modulator that interfaceswith the communication channel. The modulator maps each receivedsequence into a symbol. In M-ary signaling, the modulator maps eachn-bit sequence into one of M=2n symbols. Data in other than binary formmay be encoded, but typically data is representable by a binary digitsequence. Often it is desired to estimate and track the channel so as tobe able to perform operations, such as channel equalization andchannel-sensitive signaling.

Orthogonal frequency division modulation (OFDM) is sensitive totime-frequency synchronization. Use of pilot tones allows channelestimation to characterize the transmission pathways. Keepingtransmitters synchronized with receivers reduces error rates oftransmission.

BRIEF SUMMARY OF THE DISCLOSURE

In one embodiment, the present disclosure provides a system adapted toestimate and track a channel for wireless orthogonal frequency divisionmodulation (OFDM) communication. The system comprises first and secondmodules. The first module is configured to receive a number of pilotsymbols arbitrarily scattered between a plurality of data symbolstransmitted via at least one transmit antenna. The number of pilotsymbols are received via a number of taps indicative of the delay andmultipath effects of the channel. The second module is configured toestimate the channel value using the plurality of received pilot symbolsand in accordance with iterative correlation of the channel taps overtime. The second module performs link scheduling using the channelvalue.

In another embodiment, the present disclosure provides a method ofestimating and tracking a channel of a wireless OFDM communicationsystem. In one step, pilot symbols are received that are scatteredbetween data symbols transmitted via at least one transmit antenna. Thepilot symbols are received via a plurality of taps indicative of thedelay and multipath effects of the channel. The pilot symbols arescattered arbitrarily among at least one of time or OFDM sub-carrier.The channel value is estimated using the plurality of received pilotsymbols and in accordance with correlation of the channel taps overtime.

In yet another embodiment, the present disclosure provides a systemadapted to estimate and track a channel for wireless OFDM communicationsystem. The system includes receiving means and estimating means. Thereceiving means receives pilot symbols arbitrarily scattered between amultitude of data symbols transmitted via at least one transmit antenna.The pilot symbols are received via taps indicative of the delay andmultipath effects of the channel. The estimating means estimates thechannel value using the plurality of received pilot symbols and inaccordance with iterative correlation of the channel taps over time. Thechannel comprises a plurality of OFDM sub-channels.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating various embodiments of the disclosure, are intended forpurposes of illustration only and are not intended to necessarily limitthe scope of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a number of communication devices adapted to communicatevia one or more wireless networks.

FIG. 2 is a high-level block diagram of some of the blocks disposed inthe transmitting end of a wireless communication system.

FIG. 3 is a high-level block diagram of some of the blocks disposed inthe receiving end of a wireless communication system.

FIG. 4 shows a multitude of pilot symbols disposed between data symbolsto enable estimation/tracking of channel characteristics, in accordancewith the present disclosure.

DETAILED DESCRIPTION OF THE DISCLOSURE

The ensuing description provides preferred exemplary embodiment(s) only,and is not intended to limit the scope, applicability or configurationof the disclosure. Rather, the ensuing description of the preferredexemplary embodiment(s) will provide those skilled in the art with anenabling description for implementing a preferred exemplary embodimentof the disclosure. It being understood that various changes may be madein the function and arrangement of elements without departing from thespirit and scope of the disclosure as set forth in the appended claims.

Specific details are given in the following description to provide athorough understanding of the embodiments. However, it will beunderstood by one of ordinary skill in the art that the embodiments maybe practiced without these specific details. For example, circuits maybe shown in block diagrams in order not to obscure the embodiments inunnecessary detail. In other instances, well-known circuits, processes,algorithms, structures, and techniques may be shown without unnecessarydetail in order to avoid obscuring the embodiments.

Also, it is noted that the embodiments may be described as a processwhich is depicted as a flowchart, a flow diagram, a data flow diagram, astructure diagram, or a block diagram. Although a flowchart may describethe operations as a sequential process, many of the operations can beperformed in parallel or concurrently. In addition, the order of theoperations may be re-arranged. A process is terminated when itsoperations are completed, but could have additional steps not includedin the figure. A process may correspond to a method, a function, aprocedure, a subroutine, a subprogram, etc. When a process correspondsto a function, its termination corresponds to a return of the functionto the calling function or the main function.

Furthermore, embodiments may be implemented by hardware, software,firmware, middleware, microcode, hardware description languages, or anycombination thereof. When implemented in software, firmware, middlewareor microcode, the program code or code segments to perform the necessarytasks may be stored in a machine readable medium such as storage medium.A processor(s) may perform the necessary tasks. A code segment orcomputer-executable instructions may represent a procedure, a function,a subprogram, a program, a routine, a subroutine, a module, a softwarepackage, a class, or any combination of instructions, data structures,or program statements. A code segment may be coupled to another codesegment or a hardware circuit by passing and/or receiving information,data, arguments, parameters, or memory contents. Information, arguments,parameters, data, etc. may be passed, forwarded, or transmitted via anysuitable means including memory sharing, message passing, token passing,network transmission, etc.

Estimation and tracking of a time-varying frequency-selective channel ina multi-carrier system is carried out in accordance with an algorithmthat uses scattered pilot tones with arbitrary, random, pseudo-random,and/or substantially random time-frequency pattern. The pilot tones havea known modulation and coding scheme such the time that they weretransmitted can be determined. The algorithm is based on a linear modelthat recursively estimates the channel value at any instance of timeusing a previous estimate of the channel together with the receivedvalues of the pilot symbols. The channel value is an indicator of thechannel, for example, channel quality indicator (CQI), signal-to-noiseratio, signal strength, or any other measurement of channel sensitivesignaling, including space-selective channel conditions. The algorithmuses a number of parameters representative of the channel loading, theratio of pilot symbols to the received noise level, and the covariancematrix of the channel estimation error. The algorithm modifies suchparameter values and the channel estimate until the modified parametervalues and the channel estimate converge to satisfy predefinedconditions. The channel value is used for link scheduling in oneembodiment.

The pilot tones have a known modulation and coding scheme such thatreceivers do not need to necessarily know when they are beingtransmitted to recognize them as pilot tones. The receivers aregeographically distributed across the wireless space such that theyserve as taps with varying propagation delay and multipath effects fromthe transmitter. A channel estimate can be iteratively determined basedupon analysis of the taps for the pilot tones. The channel estimate canbe used for link scheduling in one embodiment.

In accordance with the present disclosure, estimation and tracking of atime-varying frequency-selective channel in a multi-carrier system iscarried out using scattered pilot tones that have an arbitrarytime-frequency pattern. The channel estimate is an unbiased estimate ofthe channel, and furthermore, the covariance matrix of the estimationerror defined by the difference between the actual and the estimatedvalue of the channel has a minimum variance. However, it is understoodthat there may be insubstantial variations around such estimates.

To estimate and track the channel, a linear model is assumed accordingto which, at any instance of time, a previous estimate of the channeltogether with the received values of the pilot symbols are used toestimate a new value for the channel. The pilot symbols may be part of atransmission protocol with which the wireless communication system isconfigured to comply and thus may be part of, e.g., the signal field.Alternatively, the pilot symbols may be extra symbols inserted betweenthe data symbols for the purpose of estimating the channel.

In one embodiment, the system may be an OFDMA system and the initialvalue assigned to the channel may have a value of zero. Theestimation/tracking algorithm uses, in part, a first parameterrepresentative of the channel loading and adapted to balancecontribution of the received pilot symbols with a previous estimate ofthe channel, a second parameter representative of the ratio of the pilotsymbols to the received noise, as well as a third parameter obtained byperforming a trace operation on a covariance matrix of the estimationerror.

In accordance with the present algorithm, the first parameter value andthe channel are updated recursively so as to arrive at new estimatevalues. The third parameter value is also updated to reflect themodified value of the first parameter. The modifications continuerecursively until the values of the first parameter, the channelestimate, and the third parameter converge so as to meet predefinedconditions.

The algorithm underlying channel estimation/tracking assumes a finitesupport of the time-domain response of the channel and uses thetime-domain correlation of the channel response related to the knownDoppler spectrum of the channel variations or an approximation thereof.The algorithm also accounts for singularities that occur in the initialphase of the channel estimation/tracking due to the limited number ofthe pilot symbols used. The algorithm provides a best-effort estimationof the channel state information through the limited number of the pilotsymbols available on the control channels of the OFDMA reverse link. Thealgorithm may be used for channel sensitive scheduling such as forwardlink beam forming or frequency sensitive scheduling.

In accordance with the present disclosure, estimation and tracking of atime-varying frequency-selective channel in a multi-carrier system iscarried out using scattered pilot tones that have an arbitrarytime-frequency pattern. Scattered pilots appear at different tones overtime and are substantially scattered across the band. The channelestimate is a substantially unbiased estimate. Furthermore, thecovariance matrix of the estimation error defined by the differencebetween the actual and the estimate value of the channel has asubstantially minimum variance.

The above algorithms and methods described above may be performed on aper antenna basis. Such that, the channel may be estimated for eachantenna. These estimates may be utilized to obtain the spatial signatureor the space-time signature of the channel. The estimates can then beutilized for providing beam forming, beam steering, or other spatialfunctionality.

The algorithm underlying channel estimation/tracking assumes a finitesupport of the time-domain response of the channel and uses thetime-domain correlation of the channel response related to the knownDoppler spectrum of the channel variations or an approximation thereof.The algorithm also accounts for singularities that occur in the initialphase of the channel estimation/tracking due to the limited number ofthe pilot symbols used. The algorithm provides a best-effort estimationof the channel state information through the limited number of the pilotsymbols available on the control channels of the OFDMA reverse link. Thealgorithm may be used for channel sensitive scheduling such as forwardlink beam forming or frequency sensitive scheduling.

FIG. 1 shows an example of a wireless network 10 being used forcommunications among transmitters/receivers 12, 14 andtransmitters/receivers 16, 18 as indicated. Each of thetransmitters/receivers 12, 14, 16, 18 may have a single or multipletransmit/receive antennas (not shown). While separate transmit andreceive antennas are shown, antennas may be used for both transmittingand receiving signals. The free space medium forming the channel throughwhich the signals are transmitted is often noisy affecting the receivedsignal. Estimates of the transmission channel's characteristics and theinterference level due to noise are often made at the receiver, whichindicative of the taps. Geographic location in the wireless space causesdiffering delays for the taps.

FIG. 2 is a simplified block diagram of an embodiment of a transmittingend of wireless transmission system 100. Wireless transmission system isshown as including, in part, an encoder 110, a space-frequencyinterleaver 120, modulators 130, 160, OFDM blocks 140, 170, and transmitantennas 150, 180. Modulator 130, OFDM block 140, and transmit antenna150 are disposed in the first transmission path 115; and modulator 160,OFDM block 170, and transmit antenna 180 are disposed in the secondtransmission path 125. Although the exemplary embodiment 100 of thewireless transmission system is shown as including only the two depictedtransmission paths, it is understood that the wireless transmissionsystem 100 may include more than two transmission paths. The datatransmitted by the transmit antennas 150, 180 are received by one ormore receive antennas of a wireless receive system. For example, pilotsymbols and data symbols are transmitted on various sub-carriers of theOFDM channel.

FIG. 3 is a simplified block diagram of an embodiment of a receiving endof a wireless receiving system 200. Wireless receiving system 200 isshown as including, in part, receive antenna 205, 255, front-end blocks210, 260, demodulators 215, 265, space-frequency deinterleavers 220,270, and decoders 225, 285. Wireless receiving system 200 is shown asincluding a pair of receive transmission paths, it is understood thatthe wireless transmission system 200 may include more than twotransmission paths. Pilot symbols and data symbols are received by thewireless receiving system 200. Each transmission path is related to aparticular sub-carrier. Analysis of the pilot symbols iteratively overtime allows characterizing the channel.

Further, the estimates may be iteratively performed for each receiverchain, e.g. a separate estimate for receptions at antenna 205 and 255.This allows for the channel to be estimated for each spatial channelbetween the transmitter and receiver. The estimates may be utilized,e.g. combined, to obtain the spatial signature or the space-timesignature of the channel from the different channels for each antenna.The estimates can then be utilized for providing beam forming, beamsteering, or other spatial functionality.

Assume an OFDM or OFDMA transmission with N orthogonal tones that arespaced by f_(s). Assume further that the transmitter sends pilot symbolsover a certain time frequency pattern known to the receiver, as shown inFIG. 4. In the following, it is assumed the total number of differentpilot tones N in the time-frequency pattern is greater than or equal tothe number of taps L of the channel, i.e., N≧L. Such a pilot patternenables estimation of a baseband channel response with up to L taps. Inthe following analysis, the effect of the excess delay is assumednegligible. It is also assumed that the channel variations over theOFDMA symbol duration T_(s)=1/f_(s) is also negligible, and that thenoise is a AWGN. Assume that the channel h_(k) is represented by thefollowing expression:

h_(k)=[h_(k)[0], h_(k)[l₁], . . . , h_(k)[l_(L-1)]]^(T)

Channel h_(k) is thus a L×1 vector of channel taps with relative delaysl₁, . . . , l_(L-1) for any given time instance t_(k). The time instancemay be representative of the channel update step, a single OFDMA symbolduration, slot or frame duration, etc. Assume further that the channelis a time-varying channel having a scalar complex Gaussian first orderchannel process, as shown below in expression (1):

h _(k) =r _(k) h _(k-1)+√{square root over (1−r _(k) ²)}ξ_(k), ξ_(k) ˜N_(c)(0,I _(L)),  (1)

In expression (1), N_(c)(•,•) represents a complex circular Gaussianvector specified by its mean and covariance matrix respectively, andI_(•) is an (•×•) identity matrix. It is further assumed that theprocess is stationary over a tracking interval so that r_(k), defined bythe following expression:

r _(k) =r(t _(k) −t _(k-1))

may be obtained from the channel variation model, e.g., its Dopplerspectrum. It is assumed that r_(k) is known.

The signal x_(k) received at step k may thus be defined as shown belowin expression (2):

x _(k) =PH[m _(k)]+η_(k), η_(k˜N) _(c)(0, 1),  (2)

where ρ²=(E_(p)/N₀) represents the pilot-to-noise ratio, H[m_(k)]represents the channel frequency response corresponding to the pilottone with index m_(k), where (0≦m_(k)<N), and η_(k) represents theobservation noise. The channel frequency response may be rewritten asshown below:

H[m_(k)]=w_(k) ^(H)h_(k)

w _(k) =w(m _(k))

w(m)=[1,e ^(r2πf) ^(c) ^(ml) ¹ ,e ^(t2πf) ^(c) ^(ml) ² , . . . , e^(t2πf) ^(c) ^(ml) ^(L-1) ]^(T)  (3)

where w_(k) represents the direction of the pilot tone with index m_(k).

In the above, it is assumed that there is one tone per step, thusenabling the channel estimate to be updated with only one pilotobservation per step, which in turn, reduces the complexity of channelestimation/tracking. It is understood, however, that when multiple tonesare observed at once, there may be multiple steps corresponding to thesame time instance t (e.g. t_(k)=t_(k-1)= . . . ). The estimate h_(k) ofthe channel at step k is defined by the following expression:

ĥ_(k)=[ĥ_(k)[0],ĥ_(k)[l₁], . . . , ĥ_(k)[l_(L-1)]]^(T)

Because it is assumed that the channel is Gaussian, its estimate ĥ_(k),is also Gaussian. The channel estimator, in accordance with the presentalgorithm, is unbiased and has a minimum variance. In the most generalcase, this enables the expected value of ĥ_(k) to coincide with theprojection of the true channel h_(k) onto the subspace spanned by thedirections w_(k) of pilot tones used in the estimation/trackingthroughout the step k. In the startup phase, this condition ensures thatno noise is collected in the subspace where no channel information isavailable. In the steady state when the present/past pilots span theentire L-dimensional space, this condition provides the followingexpression:

E{ĥ_(k)}=h_(k)

Accordingly, the channel estimate may be defined as below:

ĥ_(k)

N_(c)(P_(k)h_(k),Q_(k))  (4)

where P_(k) is the projector onto the subspace spanned by the availablepilot directions, as shown below:

span{P_(k)}=span{w₁,K,w_(k)}

and Q_(k) is the covariance matrix of the estimation errorΔh_(k)=(ĥ_(k)−P_(k)h_(k)).

The variance of the estimate of the channel response H[m] correspondingto ĥ_(k) and evaluated at data tones m∉Ω_(D) is represented below byĤ_(k)[m], and the present algorithm seeks to minimize the averagevariance of Ĥ_(k)[m]. The following expression (5) applies to amulticarrier system:

$\begin{matrix}{{{\Omega_{D}}^{- 1}{\sum\limits_{m \in \Omega_{D}}{{{{\hat{H}}_{k}\lbrack m\rbrack} - {H\lbrack m\rbrack}}}^{2}}}\overset{N_{D}\rightarrow\infty}{\rightarrow}{{Tr}{\left\{ Q_{k} \right\}.}}} & (5)\end{matrix}$

The exact equality in expression (5) holds when the set Ω_(D) of datatones coincides with the whole set of tones: Ω_(D)={1, . . . , N}. Theasymptotic equivalent in expression (5) holds whenever the data tonesare evenly distributed over the whole spectrum. With an appropriatedesign of the time-frequency pilot pattern and assuming a wide sensestationary channel process, the estimation/tracking provides a steadyphase covariance matrix Q_(∞), which equals a scaled identity, therebyensuring the minimum worst case variance in the steady phase.

Linear estimate ĥ_(k) of h_(k) combines the pilot observation x_(k) aswell as the estimate ĥ_(k-1) obtained at the previous step and isdefined as shown below in expression (6)

ĥ _(k) =A _(k) w _(k) x _(k) +r _(k) B _(k) ĥ _(k-1)  (6)

Using expressions (1)-(4), Linear estimate ĥ_(k), may be written asbelow:

$\begin{matrix}{h_{k} = {\frac{\left( {{\rho \mspace{11mu} A_{k}w_{k}w_{k}^{H}} + {B_{k}P_{k - 1}}} \right)h_{k}}{{mean}\mspace{14mu} {value}} + \frac{\left( {{A_{k}w_{k}\eta_{k}} + {r_{k}B_{k^{\Delta}}h_{k}} - {\sqrt{1 - r_{k}^{2}}B_{k}P_{k - 1}\xi_{k}}} \right)}{error}}} & (7)\end{matrix}$

Linear estimator (7) is shown as including expressions representative ofthe mean and error values. Assume without loss of generality that A_(k)is full rank. Accordingly A_(k) may further be defined as follows:

A _(k)=(ρw _(k) w _(k) ^(H) +A _(k) ⁻¹ B _(k) P _(k-1))^(#)  (8)

where (•)^(#) denotes Moore-Penrose pseudo inverse operator. To simplifythe estimation algorithm further, assume a class of linear estimatorsdefined as shown below:

B_(k)=γ_(k)A_(k)  (9)

where the loading parameter γ_(k) is a non-negative scalar that balancesthe contribution by the current pilot against those by the previouschannel estimate ĥ_(k-1). This simplification avoids the computationalcomplexity. Linear estimator ĥ_(k) may thus be written as shown below:

ĥ _(k)=(ρw _(k) w _(k) ^(H)+γ_(k) P _(k-1))^(#)(w _(k) x _(k)+γ_(k) r_(k) ĥ _(k-1))  (10)

An update rule for γ_(k) and the resulting estimation accuracyquantified by Tr{(Q_(k)} is developed below, where Q_(k) is thecovariance matrix of the error term in expression (7), and Tr is a traceoperator. Using expressions (1), (2), (4), (7),(9) and (10), thefollowing recursion is obtained:

Q _(k) =A _(k)(w _(k) w _(k) ^(H)+γ_(k) ² r _(k) ² Q _(k-1)+γ_(k) ²(1−r² _(k))P _(k-1))A _(k)  (11)

A _(k)=(ρw _(k) w _(k) ^(H)+γ_(k) P _(k-1))^(#)  (12)

To determine a value for γ_(k) during the startup phase, it is assumedthat P_(k-1)<I_(L) in expression (11). It is also assumed that in thestartup phase, every pilot tone contributes with a new direction to thechannel estimate; this condition requires the following:

m_(k)∉{m₁, . . . , m_(k-1)}

span{P_(k-1)}⊂span{P_(k)}, k=1, . . . , L.

thus leading to the following result:

$\begin{matrix}\begin{matrix}{\Delta_{k}^{2} = {{TR}\left\{ Q_{k} \right\}}} \\{= {{\left( {1 - r_{k}^{2}} \right)L} + {r_{k}^{2}{Tr}\left\{ Q_{k - 1} \right\}} + \frac{{w_{k}^{H}\left( {{\left( {1 - r_{k}^{2}} \right)I_{L}} + {r_{k}^{2}Q_{k - 1}}} \right)}w_{k}}{{w_{k}^{H}\left( {I_{L} - P_{k - 1}} \right)}w_{k}}}}\end{matrix} & (13)\end{matrix}$

Expression (13) is invariant with respect to the loading parameterγ_(k). A single observation (e.g. x_(k)) can provide an estimate of asingle degree of freedom. In the startup phase, appending an extra pilotresults in adding an extra direction to the channel estimate since theinclusion span{P_(k-1)}⊂span{P_(k)} takes place. In other words, thevalue of x_(k) is transformed into the estimate of the scaling appliedto the orthogonal projection of the normalized version of w_(k) onto thesubspace which is the orthogonal complement of P_(k-1) to the entirespace. Since the old estimate ĥ_(k-1) is within the span of P_(k-1), thebalancing between the new pilot contribution and the old estimate has noeffect. This enables loading factor γ_(k) to be chosen arbitrarily inthe startup phase. In particular, γ_(k) may be selected so as to have arelatively small value. One advantage of such values for γ_(k) is theelimination of pseudo-inverse operations, as shown below:

${\left( {{\rho \; w_{k}w_{k}^{H}} + {\gamma_{k}P_{k - 1}}} \right)^{\#}\left( {{w_{k}x_{k}} + {\gamma_{k}r_{k}{\hat{h}}_{k - 1}}} \right)}\overset{\gamma_{k}\rightarrow 0}{\rightarrow}{\left( {{\rho \; w_{k}w_{k}^{H}} + {\gamma_{k}I_{L}}} \right)^{- 1}{\left( {{w_{k}x_{k}} + {\gamma_{k}r_{k}{\hat{h}}_{k - 1}}} \right).}}$

Linear estimator ĥ_(k) may thus be written as shown below:

ĥ _(k)=(ρw _(k) w _(k) ^(H)+γ_(k) I _(L))⁻¹(w _(k) x _(k)+γ_(k) r _(k) ĥ_(k)),  (14)

where the loading γ_(k) is set to a small value in the startup phase,where k=1, . . . , L.

The matrix inversion operation in expression (14) may be efficientlycarried out due to the matrix inversion lemma. The resulting simplifiedupdate of the estimator ĥ_(k) is shown in following expression (15) thatis used to provide an estimate of and track the channel:

$\begin{matrix}{{{\hat{h}}_{k} = {\left( {I_{L} - {\frac{{\rho\beta}_{k}}{1 + {{\rho\beta}_{k}L}}w_{k}w_{k}^{H}}} \right)\left( {{\beta_{k}x_{k}w_{k}} + {r_{k}{\hat{h}}_{k - 1}}} \right)}},} & (15)\end{matrix}$

where β_(k)=γ_(k) ⁻¹. Selection of the loading factor γ_(k), orequivalently β_(k)=γ_(k) ⁻¹, during the steady phase k>L is describedfirst. After performing relevant algebra, an analog of expression (13)in the steady phase provides the following recursions:

$\begin{matrix}{Q_{k} = {{\frac{\left( {1 - \mu_{k}} \right)^{2}}{\rho^{2}L}\Pi_{k}} + {\left( {\Pi_{k}^{\bot} + {\mu_{k}\Pi_{k}}} \right)\left( {{r_{k}^{2}Q_{k - 1}} + {\left( {1 - r_{k}^{2}} \right)I_{L}}} \right)\left( {\Pi_{k}^{\bot} + {\mu_{k}\Pi_{k}}} \right)}}} & (16)\end{matrix}$

where:

$\begin{matrix}{{\mu_{k} = \frac{1}{1 + {\beta_{k}L}}},{\Pi_{k} = {{w_{k}}^{- 2}w_{k}w_{k}^{H}}},{\Pi_{k}^{\bot} = {I_{L} - \Pi_{k}}}} & (17)\end{matrix}$

The exact minimization of Tr{Q_(k)} with respect to parameter β_(k) iscomplicated because of the non-trivial relationship between theeigenstructure of Q_(k) and the structure of the projectors Π_(k) andΠ_(k) ^(⊥). As described above, in a steady mode, Q_(k) should convergeto a scaled identity matrix, based on the assumptions of thetime-frequency structure of the pilot and stationary channel process.Over any substantial number of steps, pilot tones are evenly distributedover the signal bandwidth. Specifically, it is assumed that for anyk₀=1, 2, . . . , the following condition applies:

$\begin{matrix}{{{1/M}{\sum\limits_{k = {k_{0} + 1}}^{k_{0} + M}{w_{k}w_{k}^{H}}}}\overset{M\rightarrow\infty}{\rightarrow}{I_{L}.}} & (18)\end{matrix}$

Condition (18) is statistically satisfied (i.e. with probability one)when a pseudo-random pilot pattern is used. With respect to the channelprocess, it is assumed that r_(k) converges to a fixed r_(∞) as kincreases. In many instances, it may be assumed that r_(k) is constant,i.e., r_(k)=r. In other instances, e.g., variable update time, r_(k) mayvary.

Assume that the sequence {w_(k)} is a process with the identitycovariance matrix. It can be shown that any quadratic form v^(H)Q_(k)v,where (∥v∥²=1), under the minimum trace criterion and the update rule(15), is a monotonic (non-increasing) sequence which is lower bounded byzero. Hence v^(k)Q_(k)v converges to a certain limit. The limits are thesame for different v. Two other observations are made. First, a steadyphase in the following form may be considered for Q_(k):

Q_(k)=Δ_(k) ²I_(L)  (19)

This enables rewriting the recursion (16) with respect to Q_(k) as anapproximate recursion with respect to Δ_(k) ², as shown below:

Δ_(k) ² I _(L)≈(r _(k) ²Δ_(k-1) ²+1−r _(k) ²)Π_(k) ^(⊥)+((r _(k)²Δ_(k-1) ²+1−r _(k) ²)μ_(k) ²+(1−μ_(k))²ρ⁻² L ⁻¹)Π_(k)  (20)

or equivalently

Δ_(k) ²≈(r _(k) ²Δ_(k-1) ²+1−r _(k) ²)(L−1)+((r _(k) ²Δ_(k-1) ²+1−r _(k)²)μ_(k) ²+(1−μ_(k))²ρ⁻² L ⁻¹)  (21)

wherein the approximation is expected to be accurate in the steadyphase.

It is desired to find β_(k)=γ_(k) ⁻¹, corresponding to μ_(k) defined inexpression (17), such that it would lead to the minimum of (21). Nearlyoptimal β_(k) and the corresponding Δ_(k) ² may be obtained as shownbelow:

$\begin{matrix}{\beta_{k} = {\rho^{- 2}\left( {{r_{k}^{2}\Delta_{k - 1}^{2}} + 1 - r_{k}^{2}} \right)}^{- 1}} & (22) \\{\Delta_{k}^{2} = {\rho^{- 2}{\beta_{k}\left( {1 - \frac{\beta_{k}}{1 + {\beta_{k}L}}} \right)}}} & (23)\end{matrix}$

The recursions defined by (22)-(23) are used to update the factor β_(k).Together with expression (15), this recursion provides estimation andtracking of the channel. The steady phase estimation error Δ_(∞) ², maybe determined by substituting recursion (22) into (23), which yields thefollowing result:

$\begin{matrix}{\Delta_{\infty}^{2} = {\left( {{r_{\infty}^{2}\Delta_{\infty}^{2}} + 1 - r_{\infty}^{2}} \right)\left( {1 - \frac{\rho^{- 2}\left( {{r_{\infty}^{2}\Delta_{\infty}^{2}} + 1 - r_{\infty}^{2}} \right)}{1 + {\rho^{- 2}\left( {{r_{\infty}^{2}\Delta_{\infty}^{2}} + 1 - r_{\infty}^{2}} \right)}}} \right)}} & (24)\end{matrix}$

It can be shown that expression (24), which is quadratic with respect toΔ_(∞) ², has a single positive root. A closed form solution toexpression (24) may be found. Table I provides a summary of channelestimation/tracking procedure described above in a pseudo-code form:

TABLE I β = β₀; for k = 1 to L${\hat{h}:={\left( {I_{L} - {\frac{\rho \; \beta}{1 + {\rho \; \beta \; L}}w_{k}w_{k}^{H}}} \right)\left( {{\beta \; x_{k}w_{k}} + {r_{k}\hat{h}}} \right)}};$end  Δ² = Δ₀ ² ; while tracking is onβ := ρ⁻²(r_(k)²Δ² + 1 − r_(k)²)⁻¹;${\hat{h}:={\left( {I_{L} - {\frac{\rho^{2}\beta}{1 + {{\rho \;}^{2}\beta \; L}}w_{k}w_{k}^{H}}} \right)\left( {{\beta \; x_{k}w_{k}} + {r_{k}\hat{h}}} \right)}};$${\Delta^{2}:={\rho^{- 2}{\beta \left( {1 - \frac{\beta}{1 + {\beta \; L}}} \right)}}};$end

The two parameters to be specified are β₀ and Δ₀ ². A relatively largevalue may be selected for β₀ (relatively small value for γ₀=β₀ ⁻¹) whileensuring a numerically stable algorithm. The value of Δ₀ ² reflects themagnitude of the estimation error at the end of the startup phase. Thecovariance matrix Q_(k) may be different from an identity matrix at theend of the startup phase, hence selection of Δ₀ ² will always be anapproximation except for a few special cases, such as when w₁, . . . ,w_(L) are orthogonal and channel variations through the startup phasecan be considered negligible. For very slow varying channels, themagnitude of the error will be proportional to ρ⁻²L⁻¹.

It is also possible to choose the initial error at the same level as theactual channel, i.e., by setting Δ₀ ²=1. Such a choice is generally morereliable because the estimation accuracy at the end of the startup phasemay vary depending on the particular sequence m₁, . . . , m_(L), ofpilots in the startup phase. A relatively large value for Δ₀ ² willresult in a somewhat slower convergence of the tracking procedure,recognizing that convergence speed may not be the overriding factor forthe best effort acquisition of the channel state information. It isunderstood, however, that an optimal selection of Δ₀ ² may be providedgiven the set m₁, . . . , m_(L).

Table 2 further simplifies the pseudo-code of Table I. Table II uses acommon initialization and does not distinguish between the startup phaseand the steady phase. This simplification has no effect on the steadyphase.

TABLE II  Δ² = 1; while tracking is onβ := ρ⁻²(r_(k)²Δ² + 1 − r_(k)²)⁻¹;${\hat{h}:={\left( {I_{L} - {\frac{\rho^{2}\beta}{1 + {{\rho \;}^{2}\beta \; L}}w_{k}w_{k}^{H}}} \right)\left( {{\beta \; x_{k}w_{k}} + {r_{k}\hat{h}}} \right)}};$${\Delta^{2}:={\rho^{- 2}{\beta \left( {1 - \frac{\beta}{1 + {\beta \; L}}} \right)}}};$end

Proper characterization of the channel process, shown in expression(24), depends on the Doppler spectrum of channel variations.Specifically,

$\begin{matrix}{{r_{k} = {r\left( {t_{k} - t_{k - 1}} \right)}},{{r(\tau)} = {\int_{- \infty}^{\infty}{{S_{D}(f)}^{i\; 2\pi \; {ft}}\ {f}}}},} & (25)\end{matrix}$

where S_(D) (f) is the power spectral density of channel variationswhich typically depends on the velocity of a mobile terminal as well asthe propagation environment. One conventional model assumes a fixedvelocity and rich scattering in the vicinity of a mobile terminal, withthe uniform azimuth distribution. The corresponding Doppler spectrum,known as the U-shaped spectrum, is defined as following:

$\begin{matrix}{{S_{D}(f)} = \left\{ \begin{matrix}{\frac{1}{\pi \; f_{D}\sqrt{1 - \left( {f/f_{D}} \right)^{2}}},} & {{f} \leq f_{D}} \\{0,} & {{{f} > f_{D}},}\end{matrix} \right.} & (26)\end{matrix}$

where f_(D)=f_(c)v_(m)/c with carrier frequency f_(c), mobile speedv_(m) and c=3.10⁸ m/s.

Another conventional model assumes a uniform spectrum defined below:

$\begin{matrix}{{S_{D}(f)} = \left\{ \begin{matrix}{\frac{1}{2f_{D}},} & {{f} \leq f_{D}} \\{0,} & {{f} > f_{D}}\end{matrix} \right.} & (27)\end{matrix}$

The time-frequency pilot pattern used herein is defined by the followingexpression:

$\begin{matrix}{k = {\left. {\sum\limits_{i = 0}^{N - 1}{a_{i,k}2^{i}}}\Rightarrow m_{k} \right. = {\sum\limits_{i = 0}^{N - 1}{a_{i,k}2^{N - 1 - i}}}}} & (28)\end{matrix}$

Such a pattern ensures a uniform coverage of the entire bandwidth overany limited time period, thereby enabling the estimation and tracking offast varying channels.

The channel estimation and tracking may be carried out using variouscodes of one or more software modules forming a program and executed asinstructions/data by, e.g., a central processing unit, or using hardwaremodules specifically configured and dedicated to determine the channeland interference level. Alternatively, the channel estimation may becarried out using a combination of software and hardware modules.

The above embodiments of the present disclosure are illustrative and notlimiting. Various alternatives and equivalents are possible. Thedisclosure is not limited by the type of encoding, decoding, modulation,demodulation, combining, eigenbeamforming, etc., performed. Thedisclosure is not limited by the number of channels in the transmitteror the receiver. The disclosure is not limited by the type of integratedcircuit in which the present disclosure may be disposed. Nor is thedisclosure limited to any specific type of process technology, e.g.,CMOS, Bipolar, or BICMOS that may be used to manufacture the presentdisclosure. Other additions, subtractions or modifications are obviousin view of the present disclosure and are intended to fall within thescope of the appended claims.

1. A method of estimating and tracking a channel of a wirelessorthogonal frequency division modulation (OFDM) communication system,the method comprising: receiving a plurality of pilot symbols scatteredbetween a plurality of data symbols transmitted via at least onetransmit antenna, wherein: said plurality of pilot symbols being subjectto channel conditions, and said plurality of pilot symbols are scatteredarbitrarily among at least one of time or OFDM sub-carrier; estimating achannel value using the plurality of received pilot symbols and inaccordance with correlation of the channel conditions over time, whereinthe channel value is defined by an initial value assigned to thechannel, and the initial value assigned to the channel value is zero. 2.The method of claim 1 wherein the channel estimate value is furtherdefined by a first parameter adapted to balance contribution of thereceived plurality of pilot symbols with a previous estimate of thechannel.
 3. The method of claim 2, wherein the channel estimate value isfurther defined by a second parameter defined by a ratio of the receivedplurality of pilot symbols to a received noise level.
 4. The method ofclaim 3 further comprising: assigning an initial value to the firstparameter.
 5. The method of claim 4 further comprising: assigning aninitial value to a third parameter defined by performing a traceoperation on a covariance matrix of an estimation error defined by adifference between the actual and the estimate value of the channel. 6.The method of claim 5 further comprising: performing a firstmodification step to modify the value of the first parameter inaccordance with the value of the third parameter; performing a secondmodification step to modify the channel estimate value in accordancewith the modified value of the first parameter; performing a thirdmodification step to modify the value of the third parameter inaccordance with the modified value of the first parameter; andcontinuing to perform the first, second, and third modification stepsuntil the values of each of the first parameter, the channel estimate,and third parameter converge to levels satisfying associated predefinedconditions.
 7. The method of claim 6 further comprising: assigning aninitial value of one to the third parameter.
 8. The method of claim 6wherein the channel estimate value satisfying the associated predefinedcondition is a substantially unbiased estimator of the channel.
 9. Themethod of claim 8 wherein the covariance matrix of the estimation erroris a substantially minimum variance estimator.
 10. An apparatus forestimating and tracking a channel of a wireless orthogonal frequencydivision modulation (OFDM) communication system, comprising: means forreceiving a plurality of pilot symbols scattered between a plurality ofdata symbols transmitted via at least one transmit antenna, wherein:said plurality of pilot symbols being subject to channel conditions, andsaid plurality of pilot symbols are scattered arbitrarily among at leastone of time or OFDM sub-carrier; means for estimating a channel valueusing the plurality of received pilot symbols and in accordance withcorrelation of the channel conditions over time, wherein the channelvalue is defined by an initial value assigned to the channel, and theinitial value assigned to the channel value is zero.
 11. The apparatusof claim 10 wherein the channel estimate value is further defined by afirst parameter adapted to balance contribution of the receivedplurality of pilot symbols with a previous estimate of the channel. 12.The apparatus of claim 11, wherein the channel estimate value is furtherdefined by a second parameter defined by a ratio of the receivedplurality of pilot symbols to a received noise level.
 13. The apparatusof claim 12 further comprising: means for assigning an initial value tothe first parameter.
 14. The apparatus of claim 13 further comprising:means for assigning an initial value to a third parameter defined byperforming a trace operation on a covariance matrix of an estimationerror defined by a difference between the actual and the estimate valueof the channel.
 15. The apparatus of claim 14 further comprising: meansfor performing a first modification step to modify the value of thefirst parameter in accordance with the value of the third parameter;means for performing a second modification step to modify the channelestimate value in accordance with the modified value of the firstparameter; means for performing a third modification step to modify thevalue of the third parameter in accordance with the modified value ofthe first parameter; and means for continuing to perform the first,second, and third modification steps until the values of each of thefirst parameter, the channel estimate, and third parameter converge tolevels satisfying associated predefined conditions.
 16. The apparatus ofclaim 15 further comprising: means for assigning an initial value of oneto the third parameter.
 17. The apparatus of claim 15 wherein thechannel estimate value satisfying the associated predefined condition isa substantially unbiased estimator of the channel.
 18. The apparatus ofclaim 17 wherein the covariance matrix of the estimation error is asubstantially minimum variance estimator.
 19. A computer readable mediumhaving a computer readable program code embodied therein, said computerreadable program code adapted to be executed to implement a method ofestimating and tracking a channel of a wireless orthogonal frequencydivision modulation (OFDM) communication system, the method comprising:receiving a plurality of pilot symbols scattered between a plurality ofdata symbols transmitted via at least one transmit antenna, wherein:said plurality of pilot symbols being subject to channel conditions, andsaid plurality of pilot symbols are scattered arbitrarily among at leastone of time or OFDM sub-carrier; estimating the channel value using theplurality of received pilot symbols and in accordance with correlationof the channel conditions over time, wherein the channel value isdefined by an initial value assigned to the channel, and the initialvalue assigned to the channel value is zero.
 20. The computer readablemedium of claim 19 wherein the channel estimate value is further definedby a first parameter adapted to balance contribution of the receivedplurality of pilot symbols with a previous estimate of the channel. 21.The computer readable medium of claim 18, wherein the channel estimatevalue is further defined by a second parameter defined by a ratio of thereceived plurality of pilot symbols to a received noise level.
 22. Thecomputer readable medium of claim 21 the method further comprising:assigning an initial value to the first parameter.
 23. The computerreadable medium of claim 22 the method further comprising: assigning aninitial value to a third parameter defined by performing a traceoperation on a covariance matrix of an estimation error defined by adifference between the actual and the estimate value of the channel. 24.The computer readable medium of claim 23 the method further comprisingperforming a first modification step to modify the value of the firstparameter in accordance with the value of the third parameter;performing a second modification step to modify the channel estimatevalue in accordance with the modified value of the first parameter;performing a third modification step to modify the value of the thirdparameter in accordance with the modified value of the first parameter;and continuing to perform the first, second, and third modificationsteps until the values of each of the first parameter, the channelestimate, and third parameter converge to levels satisfying associatedpredefined conditions.
 25. The computer readable medium of claim 24 themethod further comprising: assigning an initial value of one to thethird parameter.
 26. The computer readable medium of claim 24 whereinthe channel estimate value satisfying the associated predefinedcondition is a substantially unbiased estimator of the channel.
 27. Thecomputer readable medium of claim 26 wherein the covariance matrix ofthe estimation error is a substantially minimum variance estimator. 28.An apparatus configured to estimate and track a channel of a wirelessorthogonal frequency division modulation (OFDM) communication system,comprising: an antenna configured to receive a plurality of pilotsymbols scattered between a plurality of data symbols transmitted via atleast one transmit antenna, wherein said plurality of pilot symbolsbeing subject to channel conditions, and said plurality of pilot symbolsare scattered arbitrarily among at least one of time or OFDMsub-carrier; and a processor configured to estimate a channel valueusing the plurality of received pilot symbols and in accordance withcorrelation of the channel conditions over time, wherein the channelvalue is defined by an initial value assigned to the channel, and theinitial value assigned to the channel value is zero.
 29. An apparatusadapted to estimate and track a channel for wireless OFDM communication,the apparatus comprising: an antenna configured to receive a pluralityof pilot symbols arbitrarily scattered between a plurality of datasymbols transmitted via at least one transmit antenna, wherein saidplurality of pilot symbols are received subject to various time delaysalong the channel; and a processing unit configured to estimate thechannel value using the plurality of received pilot symbols and inaccordance with iterative correlation of the time delays over time, andperform link scheduling using the channel estimate value, wherein thechannel estimate value is defined by an initial value assigned to thechannel, and the channel estimate value is further defined by a firstparameter adapted to balance contribution of the received plurality ofpilot symbols with a previous estimate of the channel.
 30. An apparatusadapted to estimate and track a channel for wireless OFDM communication,the apparatus comprising: an antenna configured to receive a pluralityof pilot symbols arbitrarily scattered between a plurality of datasymbols transmitted via at least one transmit antenna, wherein saidplurality of pilot symbols are received subject to various time delaysalong the channel; and a processing unit configured to estimate thechannel value using the plurality of received pilot symbols and inaccordance with iterative correlation of the time delays over time, andperform link scheduling using the channel estimate value, wherein thechannel estimate value is defined by an initial value assigned to thechannel, and the channel estimate value is further defined by a ratio ofthe plurality of received pilot symbols to a received noise level. 31.The apparatus of claim 30 wherein the channel estimate value is furtherdefined by a first parameter adapted to balance contribution of theplurality of received pilot symbols with a previous estimate of thechannel, the processing unit further configured to assign an initialvalue to the first parameter.
 32. The apparatus of claim 31, theprocessing unit further configured to assign an initial value to a thirdparameter defined by performing a trace operation on a covariance matrixof an estimation error defined by a difference between the actual andestimated value of the channel.
 33. The apparatus of claim 32, whereinthe ratio of the plurality of received pilot symbols to the receivednoise level forms a first parameter, and further wherein the processingunit is further configured to: perform a first modification step tomodify the value of the first parameter in accordance with the value ofthe third parameter; perform a second modification step to modify thechannel estimate value in accordance with the modified value of thefirst parameter; perform a third modification step to modify the thirdparameter value in accordance with the modified value of the firstparameter, and continue to perform the first, second, and thirdmodification steps until the values of each of the first parameter, thechannel estimate, and the third parameter converge to levels satisfyingassociated predefined conditions.
 34. The apparatus of claim 33, theprocessing unit further configured to assign an initial value of one tothe third parameter.
 35. The apparatus of claim 32 wherein thecovariance matrix of the estimation error is a substantially minimumvariance estimator.
 36. The apparatus of claim 34 wherein the channelestimate value is further defined by the frequency response of thechannel.
 37. A computer readable medium having a computer readableprogram code embodied therein, said computer readable program codeadapted to be executed to implement a method of estimating and trackinga channel of a wireless orthogonal frequency division modulation (OFDM)communication system, the method comprising: receiving a plurality ofpilot symbols scattered between a plurality of data symbols transmittedvia at least one transmit antenna, wherein: said plurality of pilotsymbols being subject to channel conditions, and said plurality of pilotsymbols are scattered arbitrarily among at least one of time or OFDMsub-carrier; estimating the channel value using the plurality ofreceived pilot symbols and in accordance with correlation of the channelconditions over time, the channel estimate value being defined by afirst parameter adapted to balance contribution of the plurality ofreceived pilot symbols with a previous estimate of the channel, a secondparameter defined by a ratio of the plurality of received pilot symbolsto a received noise level, and a third parameter defined by performing atrace operation on a covariance matrix of an estimation error.